G is a weight-transit periodic graph.
Furthermore, it is natural to assume that our input graph is a weight-transit periodic graph.
Our result can be also applied to the case when the input periodic is not a weight-transit periodic graph.
We will use our assumption that the input periodic graph is a weight-transit graph in the following theorem.
(Weight-Transit Periodic Graph) Let (mathcal {G} = (mathcal {V}, mathcal {E}, mathrm {w})) be a static graph of a 1-dimensional periodic graph G. If, for all (e^{(t)} = (i^{(t)}, j^{(t)}, langle g^{(t)} rangle ) in mathcal {E}), (mathrm {w}left( e^{(t)}right) = g^{(t)}), then G is a weight-transit periodic graph.
We assume the our input periodic graph G (or (mathcal {G})) must satisfy the following conditions: 1 G is a positive periodic graph, and 2 G is a weight-transit periodic graph.
When the given periodic graph is weight-transit, we will argue in the next subsection that, for all (i > ell), (c_{i,r,v,v'} = 1) if (((v', langle i - r rangle ), (v,langle i rangle )) in E) and ((v', langle i - r rangle )) are reachable from s. Otherwise, (c_{i,r,v,v'} = 0).
Its physicomechanical properties (compressive strength, point loading index, unit weight, ultrasonic transit speed, water adsorption, porosity, heat and sound conductivity and sound insulation and neutron shielding effectiveness) were compared with the commercial lightweight construction bricks (normal brick, sandwich brick, gas concrete and pumice block).
Long-term mechanical ventilation (that is, 72 hours), either in normocapnia or hypercapnia, did not have consequences on body weight, intestinal transit, diuresis (data not shown) or hemodynamic variables (Table 1).
After intraperitoneal administration of GIP (50 nmol/kg body weight), small intestinal transit was inhibited to 40% in both wild-type and GLP-1 receptor-deficient mice.
Fibres are water-holding and therefore will increase stool weight; however, colonic transit time is reduced because of stimulation of peristalsis [ 23, 24].
